Yes! I've been battling it since I found out I was pregnant. Prune juice is my best friend.
What also helps is intalling one of those electronic toilet seats wtih the water jets, if you can afford one. The warm water and massage helps you go and makes it easier to go.
Yes it's normal. Digestion slows down when you're pregnant. I had to eat Raisin Bran ceral on a regular basic to help me along.